How to Use Coulomb's Law Calculator
This electric force calculator enables you to determine the repulsive or attractive force between two static charged particles using Coulomb's Law. You can also solve for any unknown variable — charge, or distance — when the other values are known.
Coulomb's Law Formula
Coulomb's law, otherwise known as Coulomb's inverse-square law, describes the electrostatic force acting between two charges. The force acts along the shortest line joining the charges:
- F — electrostatic force (Newtons)
- q1, q2 — magnitudes of the two charges (Coulombs)
- r — distance between the charges (meters)
- ke — Coulomb's constant = 8.98755 × 109 N·m²/C²
Simply select what you want to calculate, enter the remaining three values, and the calculator will instantly give you the result.
Interpretation of Results
- Positive force (F > 0) — the interaction is repulsive: the charges push each other away. This occurs when both charges have the same sign (both positive or both negative).
- Negative force (F < 0) — the interaction is attractive: the charges pull each other together. This occurs when the charges have opposite signs.
Electric Charge Units
The SI unit of electric charge is the Coulomb (C), defined as the charge transported by a constant current of 1 ampere in 1 second (1 C = 1 A × 1 s). In practice, charges are often very small, so these sub-units are commonly used:
| Unit | Symbol | Value in Coulombs |
|---|---|---|
| Millicoulomb | mC | 10−3 C |
| Microcoulomb | µC | 10−6 C |
| Nanocoulomb | nC | 10−9 C |
| Picocoulomb | pC | 10−12 C |
The default unit in this calculator is nanocoulombs (nC), because typical laboratory charges are on the order of 10−6 to 10−9 C.
Distance Units — Metric and Imperial
The calculator supports both metric and American (imperial) units for distance:
| System | Units available |
|---|---|
| Metric | meter (m), centimeter (cm), millimeter (mm), kilometer (km) |
| Imperial | foot (ft), inch (in), yard (yd), mile (mi) |
Force Units
Results are displayed in multiple force units simultaneously:
- Newton (N) — SI unit
- Kilonewton (kN) — 1 kN = 1,000 N
- Meganewton (MN) — 1 MN = 1,000,000 N
- Pound-force (lbf) — American unit, 1 lbf ≈ 4.448 N
- Dyne (dyn) — CGS unit, 1 N = 105 dyn
Conditions for Valid Results
Three main conditions must be satisfied for Coulomb's Law to return valid values:
- Stationary charges — the charges must not move relative to each other.
- Point charges — the calculation assumes point charges (or spherically symmetric charge distributions, such as a uniformly charged metal sphere).
- Non-overlapping charges — the charges must be distinct and separated by a positive distance.
Frequently Asked Questions
What is Coulomb's constant?
Coulomb's constant ke = 8.98755 × 109 N·m²/C² is a proportionality factor in Coulomb's law. It is related to the permittivity of free space: ke = 1 / (4πε0).
What does a negative force mean?
A negative result means the force is attractive — the two charges are pulled toward each other. This happens when one charge is positive and the other is negative.
Can I calculate the charge if I know the force?
Yes! Select "Find Charge q₁" or "Find Charge q₂" from the "Solve for" dropdown, enter the known force, the other charge, and the distance, and the calculator will find the unknown charge.
Can I calculate the distance between charges?
Yes! Select "Find Distance (r)", enter the force, and both charges, and the calculator will compute the distance.
Why is nanocoulombs the default unit?
The typical magnitude of electric charges in experiments and everyday scenarios is 10−6 to 10−9 C, making nanocoulombs (nC) a convenient default. You can always change the unit to Coulombs or any other unit.